Leonhard Euler

Leonhard Euler (pronounced Oiler) was born on April 15, 1707 and died on September 7, 1783. He was a Swiss mathematician who was tutored by Johann Bernoulli. He worked at the Petersburg Academy and Berlin Academy of Science. He had a phenomenal memory, and once did a calculation in his head to settle an argument between students whose computations differed in the fiftieth decimal place. Euler lost sight in his right eye in 1735, and in his left eye in 1766. Nevertheless, aided by his phenomenal memory (and having practiced writing on a large slate when his sight was failing him), he continued to publish his results by dictating them. Euler was the most prolific mathematical writer of all times finding time (even with his 13 children) to publish over 800 papers in his lifetime. He won the Paris Academy Prize 12 times. When asked for an explanation why his memoirs flowed so easily in such huge quantities, Euler is reported to have replied that his pencil seemed to surpass him in intelligence. François Arago said of him "He calculated just as men breathe, as eagles sustain themselves in the air" (Beckmann 1971, p. 143; Boyer 1968, p. 482).

One of the most famous and appealing equations, `e^{i\pi} + 1 = 0` (where `e` is Euler's number, the base of the natural logarithm, `i` is the imaginary unit, one of the two complex numbers whose square is negative one (the other is `-i`), and `\pi` is pi, the ratio of the circumference of a circle to its diameter) was derived by him.

Mathematical Association of America (MAA)

The Mathematical Association of America is the largest professional society that focuses on mathematics accessible at the undergraduate level. Our members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. We welcome all who are interested in the mathematical sciences.

International Mathematical Olympiad

The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country. The first IMO was held in 1959 in Romania, with 7 countries participating. It has gradually expanded to over 90 countries from 5 continents. The IMO Advisory Board ensures that the competition takes place each year and that each host country observes the regulations and traditions of the IMO.

William Lowell Putnam Mathematics Competition

The William Lowell Putnam Mathematics Competition is a North American math contest for college students. Each year on the first Saturday in December, over 2000 students spend 6 hours (in two sittings) trying to solve 12 problems. Individual and team winners (and their schools, in the latter case) get some money and a few minutes of fame.

The Putnam exam problems and solutions can be found here.

GeoGebra

GeoGebra is a free and multi-platform dynamic mathematics software for schools that joins geometry, algebra and calculus. It received several international awards including the European and German educational software awards.

Create a Graph

The National Center for Education Statistics (NCES), located within the U.S. Department of Education and the Institute of Education Sciences, is the primary federal entity for collecting and analyzing data related to education. A couple of interesting links that they have are a couple of sites to create graphs with flash and without.

Cartoon

Console Calculator

Console Calculator is a fast and powerful command-line calculator. This calculator performs advanced mathematical functions, remembers recent entries, allows creation of user defined variables and custom functions. This calculator is an especially handy tool for software developers or engineering.

muParser

muParser is an extensible high performance math parser library. It is based on transforming an expression into a bytecode and precalculating constant parts of it.

MathsNet

MathsNet is an interactive website for learning mathematics. They also have a wide variety of mathematical games and puzzles.

WisWeb

WisWeb is the website of the Freudenthal Institute for Science and Mathematics for secondary education (students of 12 to 18 years old). The main focus of the site are applets; small computer programs that run over the internet.

TiddlyMath

TiddlyMath is a web notebook for mathematics. It allows you to create math formulas, diagrams and graphs to display on the web.

Many Eyes

You can explore data using your eyes! This site is set up to allow the entire internet to upload data, visualize it, and talk about their discoveries with other people.

Goldbach Weave

Check out Andy Wardley's website for an explanation of the Goldbach Weave.

Emprise JavaScript Charts

EJSChart is a 100% pure JavaScript charting solution.

Jmath

Jmath is a Computer Algebra System (CAS) targeted at high school students. This one uses Java, but is reasonably fast.

QPlot

QPlot is a nifty little application that allows you to visualize scatter data by entering or digitizing them.

The Perfect Circle

Rumor has it that they hold competitions for who can draw the most perfect circle by hand. No proof of this yet, but watch this video to be impressed.

Math Forum

My Math Forum: for a better understanding of mathematics.

Magic Number Machine

Magic Number Machine is a free, full-featured, graphically laid out, high-precision, scientific calculator for Mac OS X 10.4 and greater. Full source-code is included with the distribution.

Ideal if you need to enter large expressions or have accurate precision. "Data" drawers allow an easy way to generate statistical data, linear regression and Gaussian elimination. The extensive support of complex numbers and hexadecimal numbers is also a significant benefit for anyone who has to work with this type of data.

Requires Mac OS X 10.4 or greater. Native Intel Mac support (universal binary). Source code requires XCode 2.2 or greater.